Question: Which of the following numbers is a multiple of 7? ${46,84,94,99,104}$
Solution: The multiples of $7$ are $7$ $14$ $21$ $28$ ..... In general, any number that leaves no remainder when divided by $7$ is considered a multiple of $7$ We can start by dividing each of our answer choices by $7$ $46 \div 7 = 6\text{ R }4$ $84 \div 7 = 12$ $94 \div 7 = 13\text{ R }3$ $99 \div 7 = 14\text{ R }1$ $104 \div 7 = 14\text{ R }6$ The only answer choice that leaves no remainder after the division is $84$ $ 12$ $7$ $84$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $84$ $84 = 2\times2\times3\times7 7 = 7$ Therefore the only multiple of $7$ out of our choices is $84$. We can say that $84$ is divisible by $7$.